Question

Найти натуральное число ,удовлетворяющее неравенство 2 1/3 <х + 1. 1/3 < 3 1/2 . Помогите с объяснением . Горим...

Answer 1

Отнимем из каждого члена двойного неравенства 1 1/3. Имеем:
2 1/3 - 1 1/3 < x + 1 1/3 - 1 1/3 < 3 1/2 - 1 1/2. Получаем: 1<x<2. Но между 1 и 2 не существует натурального числа.
Ответ: решений нет.

Answer 2

Solving the Inequality 2 1/3 < x + 1 < 3 1/2

To find a natural number that satisfies the inequality 2 1/3 < x + 1 < 3 1/2, we can break it down into two separate inequalities and solve for x.

Solving 2 1/3 < x + 1

First, let's solve the inequality 2 1/3 < x + 1.

Subtracting 1 from both sides gives us: 2 1/3 - 1 < x

Converting 2 1/3 to an improper fraction: 7/3 - 1 < x 7/3 - 3/3 < x 4/3 < x

So, the first part of the inequality is 4/3 < x.

Solving x + 1 < 3 1/2

Next, let's solve the inequality x + 1 < 3 1/2.

Subtracting 1 from both sides gives us: x < 3 1/2 - 1

Converting 3 1/2 to an improper fraction: 7/2 - 2/2 < x 5/2 < x

So, the second part of the inequality is 5/2 < x.

Combining the Inequalities

Now, we need to find a natural number that satisfies both inequalities. This means finding a natural number greater than 4/3 and less than 5/2.

The natural number that satisfies both inequalities is 2.

Therefore, the natural number that satisfies the inequality 2 1/3 < x + 1 < 3 1/2 is 2.